The lost deposit in Henley is little surprise, though the shock of fifth place may have been less down to the anticipated Lib Dem byelection squeeze than Labour voters staying away.

Labour's sombre mood reflects the economy, the opinion polls and the helpful advice to admit that the game is up. But there is a growing sense in the party of how Labour must act now, and how Brown's second year in power could yet be different from his first.

First, get on and govern. The Brown government has a majority of more than 60 and can choose how to use its power to act. Comparisons with previous political "sea change" moments are flawed. This week's retrospectives have emphasised the "election that never was". It was a major tactical mistake leading to the sharp reversal in political momentum. Does anybody really think this belongs in the same government-wrecking category as the ERM crisis, the winter of discontent or the Wilson devaluation? More importantly, neither Jim Callaghan in 1977 nor John Major in 1995 had any effective parliamentary majority. Both faced ideological schisms over the fundamental direction of their governments, with the emerging Bennite challenge to Callaghan and the Eurosceptic guerrilla action against Major. (With respect to John McDonnell, there is nothing like that today).

Second, simplify the message. The government has a plan for every issue – as every government must. But political recovery will not come from more policy, more initiatives and more legislation. What is needed is a much sharper public argument about what the government wants to change about Britain or why. It needs three – at most five – flagship issues to make up a concrete agenda which answers Polly Toynbee's question: what Labour is for and what it is against.

Labour must again be the fairness party, or it is nothing. Labour can win elections when it convinces a sufficiently broad range of voters, across different classes, that a fairer Britain is good for us all – that tackling inequality is not a threat to prosperity, but that an agenda for a strong economy and the good society must go together. That is tested in an economic downturn. But it is also a moment to make a clear case for collective security and sharing the risks. We are about to celebrate the 60th anniversary of the NHS – the best insurance policy in the world. Labour's core argument is that we are all in this together.

Of course, nobody is against fairness, least of all David Cameron's shiny New Conservatism. Fine, but Labour must stand for doing something about it. Cameron argues that he is now the true progressive because he knows it is not the state's job to act on inequality, climate change or international development. One day, we may find out what – if anything - this amounts to. (As one Tory thinker told me, "I can never quite remember if we're promising 'progressive means to conservative goals' or 'conservative means to progressive goals'.")

Labour's argument must be the opposite: "fairness doesn't happen by chance." This means making Labour's case for the enabling role of government if we intend the talk about equal opportunity to mean something. That was Brown's theme in addressing education and social mobility this week. Labour needs to pick political fights over opportunity and tackling child poverty, rather than detention powers for suspected terrorists.

New Labour is routinely accused of political timidity. But it was the party of the minimum wage, the windfall tax for youth unemployment, of making the case for taxation to pay more extra investment in the NHS, and combining its championing of aspiration with a distaste for rewards for failure and fat cattery at the top. A "popular fairness" agenda must find that voice again and gives it practical focus would provide some important tests of those who believe that adopting the rhetoric of tackling inequality is consequence free.

Third, Brown must be bolder about "change". A year ago, Brown represented continuity and change, but knew that he must stand for change to renew a decade-old government. A large part of the problem is that he has yet to clearly define what change he stands for.

There have been some major policy changes – the climate change bill and raising the education leaving age are the type of reforms which long outlive any government. But there has been little on a scale which resonates now with the broader public. That is especially true on those issues where the public would have most responded to a symbolic break with the Blair legacy – trust in politics, and foreign policy.

On foreign policy, the ditching of the language of a "war on terror" and advocacy of a "new multilateralism" offered signs of change. The government has been maintaining international pressure to take the Millennium Development Goals more seriously, to complete a pro-development Doha trade round, and to ensure the 2009 Copenhagen summit does make a global compact on climate change possible. Few of these issues have captured political headlines. There was always going to be a waiting game, with President Bush still in office until next January. But greater clarity about withdrawing Britain's military presence from Iraq, and about how an inquiry would then proceed, would be important in paving the way for the international agenda we need next year.

Brown's promising start on democratic renewal seems to have turned into a tidying-up exercise. Sceptics will say all of this will appeal only to political anoraks. So why not surprise the most sceptical voter? Labour could propose a ban on all outside earnings for MPs as part of a broader agenda for better politics. An elected second chamber would remove the last hereditary peers born into parliament.

Electoral reform and a clean break on party funding would both have been much better pursued from a position of political strength. The chance may simply have been missed last summer and Autumn. Rescuing them now depends on being able to rebut the charge of acting from short-term partisan advantage. Brown should look again at the idea of a citizen's constitutional convention. The civil service will be horrified. Many ministers may be too. But, as with Bank of England independence, restoring trust may now depend on politicians being seen to give away power. It would not be an agenda which was completed in a year or two – but it could result in a historic reform.

Finally, Labour worries too much about how it wants to define its opponents. Is the argument that the Tories still stand for Thatcherism, or that they stand for nothing? However, the public is not going to ask Labour what it should think of the Conservatives. There is only one fundamental way in which Labour can help to test the public definition of the Conservatives – and that is to be much clearer about how Labour is defining itself.

David Cameron is New Labour's achievement. If New Labour was simply Thatcherite, there would be no minimum wage, civil partnerships, higher public spending or devolution to come to terms with. That he can get away with such vagueness is New Labour's weakness too. But Labour will never extract any greater clarity until we realise that we must test this would-be progressive Toryism from its left, not its right.

And Cameron is a conservative. If we have done something he opposed at the time, he may well leave it in place. If we have not done it, then don't hold your breath waiting for the new Tory progressives to act.

Could this yet be Brown's second year? What can not be in doubt is that Labour would respond to Brown governing with conviction as many expected a year ago. One question being asked in the Labour party from parliament to the grassroots is "if not now, when?"

The choice is between defeatism and disunity – or spending two years governing, entrenching and Tory-proofing Labour's legacy. That offers the only route to having a fighting chance at the next election. It is always possible to do the right thing, even if all of the possible alternatives had to be exhausted first.